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If $ x = \ln (\sec \theta + \tan \theta), $ show that $ \sec \theta = \cosh x. $

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Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 11

Hyperbolic Functions

Derivatives

Differentiation

Campbell University

Oregon State University

Baylor University

University of Michigan - Ann Arbor

Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

44:57

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

03:04

Show that\begin{equati…

03:13

$\begin{array}{ll}{\text {…

03:25

If $x=\ln \tan \left\{\fra…

01:05

01:45

Prove the identity.$$\…

we know that we can rewrite this as 1/2 times e to the X plus e to the negative box. Therefore, using the pipe Iram identity of one plus tan squirt of data is equivalent to seek it. Square data. We have 1/2 times two seek it, beta. Therefore, we know that coastline H of X is the same thing as seeking data.

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